Computing parametric rational generating functions with a primal Barvinok algorithm

Computations with Barvinok's short rational generating functions are traditionally being performed in the dual space, to avoid the combinatorial complexity of inclusion--exclusion formulas for the intersecting proper faces of cones. We prove that, on the level of indicator functions of polyhedra, there is no need for using inclusion--exclusion formulas to account for boundary effects: All linear identities in the space of indicator functions can be purely expressed using half-open variants of the full-dimensional polyhedra in the identity. This gives rise to a practically efficient, parametric Barvinok algorithm in the primal space.Comment: 16 pages, 1 figure; v2: Minor corrections, new example and summary of algorithm; submitted to journa

Search-based 3D Planning and Trajectory Optimization for Safe Micro Aerial Vehicle Flight Under Sensor Visibility Constraints

Safe navigation of Micro Aerial Vehicles (MAVs) requires not only obstacle-free flight paths according to a static environment map, but also the perception of and reaction to previously unknown and dynamic objects. This implies that the onboard sensors cover the current flight direction. Due to the limited payload of MAVs, full sensor coverage of the environment has to be traded off with flight time. Thus, often only a part of the environment is covered. We present a combined allocentric complete planning and trajectory optimization approach taking these sensor visibility constraints into account. The optimized trajectories yield flight paths within the apex angle of a Velodyne Puck Lite 3D laser scanner enabling low-level collision avoidance to perceive obstacles in the flight direction. Furthermore, the optimized trajectories take the flight dynamics into account and contain the velocities and accelerations along the path. We evaluate our approach with a DJI Matrice 600 MAV and in simulation employing hardware-in-the-loop.Comment: In Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Montreal, Canada, May 201

Synthetic biology—putting engineering into biology

Synthetic biology is interpreted as the engineering-driven building of increasingly complex biological entities for novel applications. Encouraged by progress in the design of artificial gene networks, de novo DNA synthesis and protein engineering, we review the case for this emerging discipline. Key aspects of an engineering approach are purpose-orientation, deep insight into the underlying scientific principles, a hierarchy of abstraction including suitable interfaces between and within the levels of the hierarchy, standardization and the separation of design and fabrication. Synthetic biology investigates possibilities to implement these requirements into the process of engineering biological systems. This is illustrated on the DNA level by the implementation of engineering-inspired artificial operations such as toggle switching, oscillating or production of spatial patterns. On the protein level, the functionally self-contained domain structure of a number of proteins suggests possibilities for essentially Lego-like recombination which can be exploited for reprogramming DNA binding domain specificities or signaling pathways. Alternatively, computational design emerges to rationally reprogram enzyme function. Finally, the increasing facility of de novo DNA synthesis—synthetic biology’s system fabrication process—supplies the possibility to implement novel designs for ever more complex systems. Some of these elements have merged to realize the first tangible synthetic biology applications in the area of manufacturing of pharmaceutical compounds.

Controlled nonuniformity in macroporous silicon pore growth

Photoelectrochemical etching of uniform prestructured silicon wafers in hydrofluoric acid containing solutions yields periodic structures that can be applied to two- and three-dimensional photonic crystals or microfluidics. Here we demonstrate experimentally macroporous silicon etching initiated by a nonuniform predefined lattice. For conveniently chosen parameters we observe a stable growth of pores whose geometrical appearance depends strongly on the spatially different nucleation conditions. Moreover, we show preliminary results on three-dimensionally shaped pores. This material can be used to realize hybrid photonic crystal structures and incorporate waveguides in three-dimensional photonic crystals